Coordination dynamics of learning and transfer across different effector systems

Coordination Dynamics of Learning and TransferAcross Different Effector Systems

J. A. S. Kelso and P.-G. ZanoneFlorida Atlantic University

If different effector systems share a common task-specific coordination dynamics, transfer and gener-alization of sensorimotor learning are predicted. Subjects learned a visually specified phase relationshipwith either the arms or the legs. Coordination tendencies in both effector systems were evaluated beforeand after practice to detect attractive states of the coordination dynamics. Results indicated that learninga novel relative phase with a single effector system spontaneously transferred to the other, untrainedeffector system. Transfer was revealed not only as improvements in performance but also as modifica-tions of each system’s initial (prelearning) coordinative landscape. What is learned, appears to be ahigh-level but neurally instantiated dynamic representation of skilled behavior that proves to be largelyeffector independent, at least across anatomically symmetric limbs.

That animals and humans can achieve the same goal usingdifferent effectors (and, conversely, different goals using the sameeffectors) attests to the generative and multifunctional nature of thecentral nervous system (CNS). A notable example is humanspeech: The fixing (Kelso & Tuller, 1983; MacNeilage, 1980) orsudden perturbation (Kelso, Tuller, Vatikiotis-Bateson, & Fowler,1984) of an articulator normally involved in the production of asound is rapidly compensated by other, putatively coupled effec-tors in such a way as to preserve the speaker’s intent. Thisso-called motor equivalence (Hebb, 1949; Lashley, 1930) has ledto the idea of a high-level, task- or function-specific structure thatdeals with action goals, relegating the details of muscle selectionand activation to lower levels, such as the spinal interneuronalsystem (for a review, see Georgopoulos, 1997). Such units ormodules are variously referred to as functional synergies or coor-dinative structures (Bernstein, 1967; Edelman, 1987; Kelso,Southard, & Goodman, 1979; Turvey, Shaw, & Mace, 1978),generalized motor programs (e.g., Rosenbaum, 1991; R. A.Schmidt & Lee, 1998), and coordinated control programs (Arbib,1990). Common features among these notions have been discussedin Kelso (1997).

The phenomenon of motor equivalence raises a number of basicissues for all theories of motor control and learning. What kind of

abstract representation underlies stable yet flexible and adaptiveskilled behavior? How does it emerge? Is this representation reallyseparable from and independent of the effector system that exe-cutes action? Can it, in fact, be interfaced to any set of effectors?Because skilled performance is the outcome of a learning process,how might such a representation be learned? How effective istransfer or generalization of a novel skill to other, untrainedeffector systems? Strangely enough, these questions—althoughquite central to theorizing in psychology (see Fodor & Pylyshyn,1988) and cognitive neuroscience (e.g., Keele, Cohen, & Ivry,1990; Seal, Riehle, & Requin, 1992)—have seldom received theempirical attention they deserve. Although there appears to begeneral support for effector-independent representations (e.g., Jor-dan, 1995; Keele, Jennings, Jones, Caulton, & Cohen, 1995), thismay well depend on the level of the representation itself (Wright,1990). For instance, intermanual transfer of writing skill from thedominant to nondominant hand or transfer of mirror writing skill(e.g., Latash, 1999) may operate at a higher, more abstract level ofrepresentation, such as the overall shape of a letter. On the otherhand, transfer of the same writing skill across effectors, such aswriting one’s name large or small (e.g., Raibert, 1977; Wright,1990), may share a common, lower level specification for theeffectors engaged. Such notions are common in current forwardand inverse “internal models” of motor control, adaptation, andlearning (e.g., Imamizu, Uno, & Kawato, 1998; Kawato,Furawaka, & Suzuki, 1987; Wolpert & Ghahramani, 2000) inwhich task variables are transformed or mapped into a space ofintrinsic (e.g., joint angles) or extrinsic (e.g., endpoint motion)control variables depending on the task context. Error feedbackfrom various sources relative to the “desired state,” as well asinternal feedback, is used as a means to update the internal modeland adjust the motor commands to the controller.

The present approach takes a slightly different tack. Building onprevious theoretical (Schoner & Kelso, 1988; Schoner, Zanone, &Kelso, 1992; Zanone & Kelso, 1994) and empirical (Zanone &Kelso, 1992, 1997; see also Fontaine, Lee, & Swinnen, 1997; Lee,Swinnen, & Verschueren, 1995; Mitra, Amazeen, & Turvey, 1998;Swinnen, Dounskaia, Walter, & Serrien, 1997) research, sensori-

J. A. S. Kelso and P.-G. Zanone, Center for Complex Systems and BrainSciences, Florida Atlantic University.

P.-G. Zanone is now at Les Unites de Formation et de RechercheSciences et Techniques des Activites Physiques et Sportives (UFRSTAPS), Universite Paul Sabatier, Toulouse, France.

This research was funded in part by National Science Foundation GrantDBS–9213995 and by National Institute of Mental Health GrantsMH42900 and KO5 MH01386. An early version of this article waspresented at the Society for Neuroscience meetings in New Orleans (No-vember 1994). We thank Collin Brown for his help with data collection.

Correspondence concerning this article should be addressed to J. A. S.Kelso, Center for Complex Systems and Brain Sciences, 3848 FAU Bou-levard, Innovation II, Florida Atlantic University, Boca Raton, Florida33431-0991. E-mail: [email protected]

Journal of Experimental Psychology: Copyright 2002 by the American Psychological Association, Inc.Human Perception and Performance2002, Vol. 28, No. 4, 776–797

0096-1523/02/$5.00 DOI: 10.1037//0096-1523.28.4.776

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motor learning is captured in terms of coordination dynamics:equations of motion that govern how a system’s coordinationstates on a given level of description evolve in time and how suchcoordination emerges from the nonlinear interaction among com-ponent subsystems under the influence of boundary conditions thatinclude perceptual, intentional, and intrinsic constraints. Such dy-namics are specified in terms of functionally or task-specificcoordination (also called collective) variables that characterize thecoordination tendencies of the system at any point in time duringthe learning process (see also Saltzman & Kelso, 1987). Coordi-nation variables, values of which define the states of the coordi-nation dynamics, have been identified in situations in which be-havior changes spontaneously under the influence of anexperimentally manipulated control parameter. Spatiotemporallyorganized behavior evolves in time according to a dynamical lawthat both captures and predicts the stability and change of coordi-nation under varying task and environmental circumstances(Kelso, 2000). In recent work, laws at the behavioral level, at leastin the case of unimanual and bimanual coordination, have beenderived from a neurobiological account based on known cellularand neural ensemble properties of the cerebral cortex, including itsheterogeneous intra- and cortico-cortical connectivity (Fuchs,Jirsa, & Kelso, 2000; Jirsa, Fuchs, & Kelso, 1998; Jirsa & Haken,1996; Jirsa & Kelso, 2000). This multilevel approach has been ableto establish an explicit connection between neural and behaviorallevels of description (Jirsa, Jantzen, Fuchs, & Kelso, 2002; Kelso,Fuchs, & Jirsa, 1999; Kelso, Jirsa, & Fuchs, 1999).

Turning to the concrete case of 1:1 coordination between twocomponent subsystems (whether the two arms, the two legs, a legand an arm, or a stimulus and a response), the coordinationdynamics has been shown to take the following form (Kelso,DelColle, & Schoner, 1990; Kelso & Jeka, 1992; see alsoAmazeen, Amazeen, Treffner, & Turvey, 1997; Bressler & Kelso,2001; Carson, Goodman, Kelso, & Elliot, 1995; Fuchs & Kelso,1994; Peper, Beek, & van Wieringen, 1995; R. C. Schmidt &Turvey, 1995):

� � �� a sin� � 2b sin2� � �Q�t . (1)

This dynamical law, in which the coordination variable, �, is therelative phase between the two components, has been progres-sively established in a series of detailed experiments beginningwith Kelso (1981, 1984) and theoretical steps initiated by Haken,Kelso, and Bunz (1985). It contains essentially three kinds ofparameters: (a) one that reflects intrinsic frequency differencesbetween the uncoupled individual components (��), (b) one thatreflects external or internal factors (control parameters) the ratio ofwhich (b:a) has been shown to govern the strength of couplingbetween the components, and (c) one that reflects that all realsystems contain noise or fluctuations (�t ) of a given strength Qthat give rise to phase variability (Kelso et al., 1990; Schoner,Haken, & Kelso, 1986). If one wishes to use Marr’s (1982) notionof representation and algorithm to describe how equivalenceclasses of processes can be described in an explicit manner, andhow several processes may use the same higher level mechanismor algorithm to accomplish a given task, then the elementarycoordination dynamics of Equation 1 clearly qualifies as an ab-stract representation of skilled behavior. For example, the stabilityproperties of coordination dynamics ensure that the learner is able

to maintain and adapt coordination patterns to changing circum-stances, one of the hallmarks of skilled behavior. In addition,because the coordination dynamics is multistable, the learner hasaccess to several coordination patterns for the same set of circum-stances, thereby providing her or him alternative solutions toaccomplish the same task. By virtue of instabilities and modifica-tions in the coordination dynamics, an additional source of gener-ativity is available to the learner, namely, the ability to select orchoose one behavioral form from another when internal or externalconditions so demand. All these features have been observed in anumber of rather different experimental model systems, attestingto the so-called universal nature of the coordination dynamics(Haken, 1996; see also Kelso, 1994a, 1994b; Turvey, 1994, forreviews).

The hypothesis that visuomotor learning may be captured at thelevel of an abstract rule or dynamical law is supported by a seriesof experiments on bimanual coordination (Zanone & Kelso, 1992,1997; see also Fontaine et al., 1997; Mitra et al., 1998; Swinnen etal., 1997) in which subjects were asked to learn a novel phaserelationship between the rhythmic motion of homologous limbs. Akey idea behind these experiments was that learning involves amodification of the learner’s preexisting capacities in the directionof the skill to be learned (Kelso, 1990). Although other theoristsalso stress that learning and development proceed in the context ofpreexisting biases (e.g., Sporns & Edelman, 1993), they have notprovided ways to evaluate this preexisting movement repertoireprior to learning. Indeed, identification of such constraints isgenerally lacking or, more usually, totally ignored in theories ofskill acquisition and development. Because discovering the natureof preexisting capabilities is so difficult, investigators have tried touse tasks that are as novel as possible and hence unrelated to anyexisting coordination tendencies that the learner might possess.Ironically, this strategy may prevent us from understanding thefeatures of the learned representation that are shared across tasksand the level at which they are specified.

In Zanone and Kelso (1992; see also Kelso, 1990), a methodwas developed to overcome the difficult problem of evaluating thepreexisting capabilities of the learner by scanning—before learn-ing begins and throughout the learning process—the space of thecoordination variable proven to be valid for this task, namely, therelative phase between the interacting components (e.g., Fuchs &Kelso, 1994; Haken et al., 1985; Kelso, 1984; R. C. Schmidt &Turvey, 1995; Swinnen et al., 1997). This allows researchers to setthe learning task on an individual basis such that it does notcorrespond to preexisting coordination tendencies that, whetherinnate or acquired, may already exist in the individual learner’srepertoire. According to our theory, new task requirements maycooperate or compete with preexisting coordination tendencies,thereby influencing the nature and rate of the learning process. Asthe task is learned, the stability of the performed pattern increases(indexed by shifts in the mean relative phase toward the learnedpattern, a sharpening of the distribution of phasing fluctuations,and faster relaxation time). At the same time, the memorizedrelative phase evolves on a slower time scale, biasing the per-formed pattern toward the to-be-learned relative phase (Schoner &Kelso, 1988; Schoner et al., 1992). An outcome of using theresearch strategy of coordination dynamics is that learning hasbeen demonstrated to not only involve the acquisition of a new

777COORDINATION DYNAMICS OF LEARNING AND TRANSFER

pattern of behavior but also to change the entire repertoire, includ-ing formerly stable behavioral patterns themselves.

In our original work (Zanone & Kelso, 1992; see also Kelso,1990, 1995, chap. 6), we showed not only that a new attractor isestablished as memorized information gains strength but also thatthe learning process may take the form of a nonequilibrium phasetransition or bifurcation: Stabilization of the learned pattern in-creased the number of coordination patterns available to thelearner and destabilized others (at least temporarily). Learning, inother words, not only altered behavior in the direction of theto-be-learned pattern but also changed the entire layout of thecoordination dynamics (see Schoner et al., 1992, for the formaldetails). Regarding the issue of task equivalence and the nature ofthe hypothesized abstract representation of sequential behavior,two additional findings are noteworthy (Zanone & Kelso, 1997).First, we found that learning a new phase relationship occurredirrespective of any time ordering between the moving fingers. Forexample, when a 90° phasing (i.e., the left finger lagging the rightby one quarter of a cycle) was learned, subjects were also able toexecute a 270° or �90° phasing pattern (i.e., the left finger leadingthe right by the same amount), even though the latter phasing hadnever been practiced. We hypothesized that such spontaneoustransfer of learning in the same coordination system may be due tothe preservation of symmetry (viz., �90°) in the underlying coor-dination dynamics.

A second result of our study (Zanone & Kelso, 1997) was thatsubjects performed the newly learned phase relationship throughdifferent kinematic realizations of the end effectors. Although thetask requirement was always met (i.e., subjects were asked toperform a given phase relationship in synchrony with a visualmodel), the way it was met kinematically ranged from smooth,quasi-sinusoidal motion of both end effectors to rather jagged,discontinuous movements. Interestingly, the kinematics adoptedfor realizing the required task were shown to depend on therelative stability of preexisting attractive states (e.g., inphase andantiphase) in the initial coordination dynamics. For example, toaccomplish a learned relative phase of 90° or 270° with the visualstimulus, subjects produced a spikelike motion of the fingers withlong pauses in the component trajectories corresponding to relativeinphase or antiphase motion (see Zanone & Kelso, 1997, Figures6 and 7). Both results, symmetry preservation at the collectivelevel and multiple realization at the end-effector level, suggestedthat learning occurs at the abstract level of the coordination dy-namics, which itself may be considered an expression of, orrepresentation for, motor or (more correctly, we think, in the caseof learning perception–action relations) functional equivalence.

In short, how a pattern learned with one set of effectors can begeneralized to others is a very important problem, the solution ofwhich will help provide a deeper understanding of skill acquisi-tion. If our hypothesis that the abstract, task-shared nature ofcoordination dynamics is at the origin of transfer of learning iscorrect, then generalization of learning should occur across differ-ent effector systems, thereby enhancing the range of functionalequivalence. This means not only that two end effectors within apair can be switched with each other (Zanone & Kelso, 1997) butalso that one pair of end effectors can be exchanged for analtogether different pair to realize the same task. Specifically, weinvestigated whether learning a novel phase relationship with oneeffector system (say, the arms) transfers spontaneously to another

effector system (say, the legs), and vice versa. It is important toemphasize in terms of the research strategy of coordination dy-namics that learning and transfer are assessed not (or not only) interms of changes in performance (cf. Latash, 1999) but rather interms of specific alterations in the layout of the coordinationdynamics underlying both effector systems. This means that coor-dination tendencies that may be present initially in both sets ofeffectors prior to learning (the so-called intrinsic dynamics, in ourterminology [Kelso, Scholz, & Schoner, 1988], or the preexistingmovement repertoire, in the terminology of Sporns & Edelman,1993) must be assessed before the introduction of a novel coordi-nation task. We predicted that transfer and generalization of learn-ing should occur across different effector systems to the extent thatthey share comparable coordination dynamics. Thus, if the hypoth-esis is correct, then both the trained and the untrained effectorcombination should simultaneously exhibit stabilization of theto-be-learned phasing pattern. Moreover, other phasing relationsare predicted to be biased toward the to-be-learned pattern if, asour theory predicts, the entire coordination dynamics is altered bythe learning process. Such a result is not typically examined inwork from other traditions, because the full range of task-relatedcoordination tendencies and how these may change with learningis not explored. That is, traditional approaches seldom measurehow other timing relations, beyond the task to be learned, areinfluenced by the learning process (for further discussion, seeR. A. Schmidt & Lee, 1998, pp. 382–383).

Whether complete transfer occurs, of course, may depend onwhether the learning task is accomplished by components that arebiomechanically similar (e.g., the two arms or the two legs) ordifferent (e.g., an arm and a leg). The extended form of thecoordination dynamics (Equation 1; Kelso et al., 1990) contains aterm (��) that respects asymmetries such as those caused bybiophysical differences between limbs (Jeka & Kelso, 1995; Kelso& Jeka, 1992; Sternad, Amazeen, & Turvey, 1996) or differencesbetween stimulus and response components (Kelso et al., 1990;Wimmers, Beek, & van Wieringen, 1992), whereas the originalform (Haken et al., 1985) does not. For reasons of methodologicalsimplicity, and because our aim was to determine the relevance ofthese concepts for the issues of transfer and generalization, wefocused on the case of learning with anatomically symmetric, butdifferent, effectors. Given the many differences of neural andbiomechanical origin between arms and legs, no one, of course,expects perfect transfer. Nevertheless, evidence that the unprac-ticed pattern is learned and stabilized would bolster the view thatcoordination dynamics constitutes a single abstract representationfor an entire equivalence class of coordinated actions, specificallythose dealing with the relative timing between coordinatingcomponents.

Method

The experiment was carried out on 2 consecutive days. On the first day,after informal familiarization with the task and the experimental setup, thecoordination dynamics pertaining to both effector systems (i.e., the armsand the legs) was probed for each subject between 0° and 180°. Noknowledge of results (KR) was provided to subjects during these scanningprobes. Then the to-be-learned pattern was set on an individual basis suchthat it did not correspond to an already-existing stable pattern (see theIndividual Data: Selecting the To-Be-Learned Pattern section for furtherdetails). This new pattern was then practiced with one effector system (i.e.,

778 KELSO AND ZANONE

either the arms or the legs) for 20 trials, with KR given at the end of eachtrial. On the second day, 20 additional practice trials of the to-be-learnedphasing pattern were administered. At the end of this training period, aprobe of the coordination dynamics was carried out again for both prac-ticed and unpracticed limb pairs.

Subjects

Eighteen naive subjects (mean age � 24.2 years), all undergraduatestudents at Florida Atlantic University, participated in the experiment andwere paid after completion of the entire experimental procedure. A pre-requisite for participation was that no visual or physical impairment im-peded perceiving or producing the required timing pattern. Twelve subjectswere assigned to two experimental groups, in which the to-be-learnedphase relationship was practiced either with the arms or with the legs. Sixcontrol subjects were not exposed to such a learning task.

Apparatus

Subjects were seated in a specially designed multi-articulator coordina-tion (MAC) apparatus (for a detailed description of the MAC, see Kelso &Jeka, 1992). Their arms rested against a pad in an almost vertical position,and the wrists were inserted into cuffs attached to shafts that rotated aboutthe elbows. The subjects’ ankles were inserted into similar cuffs, attachedto shafts rotating about the knees. Motion of the four limbs was therebyrestricted to single-joint flexion and extension motion in the parasagittalplane. The apparatus allowed subjects to move their limbs as freely aspossible, with no abutment and negligible friction. The angular displace-ments of all four limbs were monitored by potentiometers. A visualmetronome, composed of two blinking light-emitting diodes (LED), waslocated in front of the subjects, 3 ft (0.91 m) away. The onset of each LEDwas controlled by a microcomputer. Various relative phases could bedisplayed by manipulating the time interval between the LED onsets whilemaintaining the period between two successive light pulses constant.Because of the difference in the limb eigenfrequencies, we set the metro-nome frequency to 0.8 Hz for the legs and to 1.1 Hz for the arms.1 Signalsfrom the visual metronome and the MAC apparatus were digitized in realtime at a sampling rate of 200 Hz. KR, when appropriate, was returned tothe subjects on a computer screen located beside the visual metronome (fordetails, see Zanone & Kelso, 1992).

Task and Procedure

Subjects were instructed to produce the required relative phase specifiedby the visual metronome as accurately as possible through appropriatelycoordinated limb movements of the arms and legs. Specifically, subjectswere required to attain exact synchronization of the right and left limbswith the onset of the ipsilateral LED. With both limb pairs, the instructionwas to time or synchronize peak motion of the limb (i.e., the top reversalpoint) precisely at the moment when the corresponding LED was turnedon. Otherwise, movement kinematics (displacement, velocity, etc.) werefree to vary.

First, a complete probe of each subject’s coordination ability was carriedout in 13 separate runs. In each such scanning run a different relative phasewas required, which varied randomly from run to run. All the multiples of15° in the interval between 0° and 180° were set to the subject, therebyscanning the entire interval between the inphase and antiphase patterns.Each scanning run lasted 18 s for the arms and 25 s for the legs; that is, 20movement cycles were performed by each effector system. On the first day,the effector system that would later practice the task was scanned first,followed by the nonpracticed system. On the second day, the scans werecarried out in the reverse order. This procedure minimized uncontrolledeffects of probing the practiced system per se on possible transfer to thenonpracticed effector system. The specific task to be learned was individ-

ually determined on the basis of subjects’ performance on the initialscanning probe (see the Results and Discussion section). That is, therelative phase pattern to be learned was chosen according to the results ofthe initial scanning probes of both effector systems, under the caveat thatto be chosen as novel, the timing pattern to be learned did not coincide withan already-existing coordination pattern.

Each learning trial lasted 20 s when practice was with the arms and 27 swhen practice was with the legs, corresponding to 22 cycles of practice pertrial for each limb pair. Practice was given in four consecutive blocks of 10trials, with an average intertrial interval of 15 s and an interblock intervalof 1 min. Note that 10 practice trials correspond to 220 attempts to producethe required phasing pattern. Every learning trial was followed by KR,which provided both qualitative and quantitative information aboutperformance.

Measures

As a matter of convention, we defined relative phase with reference toright-hand side events. Thus, metronome and movement patterns in whichthe right event led with respect to the left were designated a positiverelative phase, that is, ranging between 0° and �180°. Conversely, left-leadphasing patterns had negative values that varied between 0° and �180° or,equivalently, positive values between �360° and �180°. Consonant withthe discrete task requirement of coinciding the movement peak with themetronome signal, our measure of the produced pattern, �, was a pointestimate of the relative phase between limb movements. The time differ-ence between the occurrence of the peak reversal point of the left limb andthat of the right limb closest in time was expressed (in degrees) relative tothe period of the corresponding right limb cycle.

Results and Discussion

We first present individual data to illustrate the steps used in theexperimental procedure, in particular, the way we selected theto-be-learned relative phase, and to provide preliminary evidencepertaining to our hypotheses regarding learning and transfer. Thenwe present group results to support the conclusions drawn fromindividual data. Finally, we present the control group data tobolster the claim that the observed effects are due to the experi-mental manipulation, namely, learning induced by specificpractice.

Individual Data: Selecting the To-Be-Learned Pattern

A central part of our experimental rationale was to choose thepattern to be learned with reference to the coordination capabilitiesof the individual learner before practice in this kind of task. In thepresent situation, such selection was more complicated than inprevious work (Zanone & Kelso, 1992, 1997), because two effec-tor systems must be probed instead of one, thereby creating thepossibility of discrepancies in their respective underlying coordi-nation dynamics. In the following, we illustrate how the to-be-learned relative phase was selected for 3 typical subjects, accord-ing to the results obtained from initial scanning probes of thecoordination dynamics.

1 The choice of a frequency specific to each effector system was anoutcome of previous pilot work. We selected the average frequency atwhich 8 pilot subjects spontaneously oscillated their arms and the legs inthe MAC apparatus.


Figure 1 shows the results of the leg and arm probes carried outbefore learning for a subject who eventually practiced 90° with thelegs. Figures 1A and 1C display the performed (solid line) andrequired (dashed line) relative phases as a function of time. Al-though randomly presented experimentally, for ease of viewing all13 scanning runs for a given pair of limb effectors are shown inincreasing order of the phasing requirement.2 Across these pla-teaus of 20 cycles each, relative phase increases by 15°, starting at0° for Step 1 and ending with 180° at Step 13, as shown by thedashed line. This provides a picture of the behavior expected hadthe phasing requirements been scaled up stepwise within a singletrial. Figures 1B and 1D show the frequency histogram of therelative phase actually performed across all phasing requirements.The modes, or dominant peaks, in the histogram reflect relativephase patterns that are produced most frequently and are indicativeof preexisting attractive coordination tendencies. One row of pic-tures (i.e., Figures 1A and 1B and Figures 1C and 1D) constitutes

the displays provided after completion of the scanning probes tothe experimenters—but not to the subject—to select the to-be-learned phasing pattern. In addition, the statistics (mean and stan-dard deviation) of the relative phase produced for each of the 13required phasings (henceforth plateau statistics) were also avail-able to the experimenters. This information allowed us to identifythe phasing patterns that were performed in a reasonably accurateand consistent fashion.

Figure 1A indicates that for the first phasing requirement of 0°(i.e., Plateau 1) the relative phase performed with the legs wasclose to 0°. Presentation of the 15° requirement first entailed anoticeable perturbation, but then performance eventually returned

2 This was the scanning procedure we had used in our previous work(Zanone & Kelso, 1992, 1997) to probe the nature of the underlyingcoordination dynamics.

Figure 1. Initial scanning probes (Day 1) of the leg and arm coordination dynamics for a typical subject whopracticed a 90° relative (rel.) phase with the legs. A and B show probes of the leg system, whereas C and D showprobes of the arm system. The left graphs display the performed (solid lines) and the required (dashed lines)relative phases. For ease of viewing, we joined together the 13 individual trials (labeled by plateau numbers) inwhich a single relative phase was required at random. The right graphs display the frequency distributions ofperformed relative phase across all phasing requirements. Both arm and leg probes revealed coordinationtendencies near 0° and 180°, suggestive of an intrinsic bistable dynamics. This probe led us to select 90° as thelearning task. deg � degrees.


to 0°. On the next required phasing (i.e., 30°), the performedrelative phase shifted to near 180° (i.e., above 150°) and fluctuatedthere for all the following task requirements. Such a phenomenon,in which behavior appears to remain trapped in the current state orswitches to another state irrespective of the actual value of the taskrequirement, reflects attraction to existing, so-called intrinsic co-ordination tendencies (Kelso, 1984) and attests to the inherentlynonlinear nature of the underlying dynamics. Figure 1B reflectsthis shift between 0° and 180°, showing two modes situated aroundthese values. Plateau statistics (not shown) revealed that the moststable phasing patterns were 9.76° and 169.11°, with standarddeviations of 5.75° and 8.16°, respectively. Thus, Figures 1A and1B suggest that the underlying dynamics for the legs are bistable,exhibiting attractive states near inphase and antiphase, with thelatter pattern somewhat less stable (more variable) than the former.A similar conclusion may be drawn from the results obtained frominitial scans of the arms. The time series (Figure 1C) and the

frequency histogram (Figure 1D) of performed relative phasesuggest that the coordination dynamics for the arm system isbistable at inphase and antiphase (more precisely, at �2.30° and180.38°, respectively), the former being more stable (SD � 4.62°)than the latter (SD � 9.44°).

The bistable nature of the coordination dynamics of both limbpairings renders the choice of the to-be-learned phasing patternquite straightforward, namely, a 90° relative phase, situated inbetween preexisting attractive states of the coordination dynamics.Overall, 4 subjects exhibited this type of bistable coordinationdynamics for both effector systems before learning. Two of thempracticed the 90° relative phase with the arms, and 2 practiced itwith the legs.

Figure 2 shows the results obtained from initial scanning probesof the legs and arms for a subject who eventually practiced 45°with the legs. Figure 2A indicates that besides performing inphaseand antiphase fairly stably for requirements close to 0° and 180°

Figure 2. Initial scanning probes (Day 1) of the leg and arm coordination dynamics for a typical subject whopracticed a 45° relative (rel.) phase with the legs. A and B show probes of the leg system, whereas C and D showprobes of the arm system. The left graphs display the performed (solid lines) and the required (dashed lines)relative phases. For ease of viewing, we joined together the 13 individual trials (labeled by plateau numbers) inwhich a single relative phase was required at random. The right graphs display the frequency distributions ofperformed relative phase across all phasing requirements. Both arm and leg probes revealed coordinationtendencies near 0°, 90°, and 180°, suggestive of multistable dynamics, which led us to select 45° as the learningtask. deg � degrees.


(cf. the left and right parts of the graph), the legs performed asubstantial number of movements about 90° for intermediate phas-ings (middle part of the graph). Accordingly, the histogram of theoverall produced relative phase (Figure 2B) exhibits three modescentered about 0°, 90°, and 180°. Plateau statistics indicated thatthe most stable patterns were near �4.75°, between 77.04° and106.26°, and between 177.05° and 186.98°. Thus, Figures 2A and2B suggest that the initial coordination dynamics for the legsystem is tristable within the 0°–180° range.3 In previous experi-mental work on bimanual learning (Zanone & Kelso, 1997), suchmultistability was identified as an alternate prototypical regime ofthe coordination dynamics.

In a similar manner, Figures 2C and 2D suggest that the armcoordination dynamics is also tristable in the 0°–180° range.Plateau statistics revealed that stable coordination patterns existedabout 4°, 85°, and 175°. Hence, the subject depicted in Figure 2was assigned to practice a 45° pattern, a relative phase locatedhalfway between preexisting attractive states of the coordinationdynamics that was not performed stably in the prelearning scan-ning probes. For the same reasons, 4 subjects practiced 45°, and 2others practiced 135°, another unstable phasing pattern situatedbetween the 90° and 180° stable states. For each requirement, halfof the subjects practiced with the legs, and the other half practicedwith the arms.

Figure 3 shows the results of the probes for the arm and legsystems, carried out before learning for a subject who eventuallypracticed a 75° relative phase with the arms. General features ofbistable coordination dynamics were present (cf. Figure 1A), ex-hibited by bimodality in the two frequency histograms (Figures 3Band 3D). Examination of the statistics for the 75° requirementperformed with the arms revealed, however, that a pattern near125° was produced in a fairly stable manner (seen also in Figure3A as a noticeable plateauing of performance). Such behavior isserendipitous, if not strange, because it is unrelated to the taskrequirement and fails to exhibit the property of attracting neigh-boring phases that typically characterizes stable behavior. There-fore, the coordination dynamics for the arm system was deemed tobe basically bistable at inphase and antiphase. Because the scan ofthe leg system (Figures 3C and 3D) also was suggestive of bi-stability, the learning task might justifiably have been set at 90°.However, because of the anomalous behavior observed for the armat 125°, the to-be-learned relative phase was moved to 75°, apattern never previously performed and totally absent in the fre-quency histogram (Figures 3B and 3D). This maximized the dis-tance between the task requirement and any preexisting coordina-tion tendencies, thereby enhancing the possibility of identifyingclear learning effects. Overall, only 2 subjects showed such atyp-ical behavior and were thus assigned to practicing 75° with thearms and with the legs, respectively.

Individual Data: Effects of Learning and Transfer

Having identified preexisting coordination tendencies in indi-vidual subjects, we now turn to the issue of how practice of theto-be-learned phasing pattern with a single effector system mayaffect the underlying coordination dynamics of both. Such modi-fications are presumed to be in the direction of the to-be-learnedpattern, provided, of course, that the learning task is mastered withpractice. Table 1 shows changes in performance accuracy and

variability between the first and last three learning trials, for the 3subjects illustrated in Figures 1–3.

For all 3 subjects, the mean error (first column) drops sharply byat least 45° between the first and last learning trials, whereas thewithin-trial standard deviation (third column) decreases by approx-imately half. Meanwhile, the between-trials fluctuations (secondand fourth columns) also diminish markedly for both scores. Thedata in Table 1 suggest that with practice, performance tends tostabilize close to the required values, a putative sign of learning.

How is the coordination dynamics modified as performanceimproves? Figure 4 shows the results of leg and arm probes,carried out after practicing a 90° relative phase with the legs, forthe same subject whose data are presented in Figure 1. In Figure4A, the time series of performed relative phase shows that afterstaying close to 0° for the first two phasing requirements, the legpattern shifts to a value of about 90°, with fluctuations increasingas the phasing requirement approaches 180° (viz., with increasingtime). The corresponding frequency histogram (Figure 4B) showstwo modes at 0° and 90°, the latter more dominant than the former.Plateau statistics revealed that the most stable patterns are per-formed between �0.28° and 0.70°, as well as in the 97.87°–101.67° range. All these features indicate that after practice, thecoordination dynamics for the leg system contains attractive statesnear 0° and 90°.

Two points need emphasis. First, because the 90° pattern wasnot a stable state of the initial leg coordination dynamics (cf.Figures 1A and 1B), its stabilization must be due to learningthrough practice. Learning a novel phasing pattern appears toestablish a new attractive state of the underlying coordinationdynamics close to the task requirement. Second, the preexistingantiphase pattern appears to destabilize (at least temporarily) as aresult of learning the 90° pattern. These two results are in line withthe results of previous research regarding initially bistable biman-ual dynamics (Zanone & Kelso, 1992, 1997; see also Fontaine etal., 1997). They suggest that the learning process essentially in-volves stabilizing unstable coordination states and destabilizingothers, thereby modifying the layout of the underlying coordina-tion dynamics.

Figures 4C and 4D reveal that arm coordination patterns arestrongly modified after practice with the legs alone. The timeseries of performed relative phase, the overall frequency distribu-tion, and the statistics suggest that attractive coordination statesexist about 0° and 90° after practice (cf. Figures 1C and 1D).Because the 90° pattern was not practiced by the arms, its stabi-lization as a novel attractive state of the arm coordination dynam-ics reflects transfer of learning from the trained leg system. Again,such transfer involves substantial alterations of the underlyingcoordination dynamics, matching well those encountered in the

3 For symmetry arguments, one has to posit that the symmetry partner of90°, namely �90° or 270°, is stable too, leading to multistable dynamics inthe entire space of the coordination variable, relative phase, which spansfrom 0° to 360°. In fact, the assumption that symmetry of the underlyingcoordination dynamics is preserved when a phasing pattern intermediate toinphase and antiphase exists either before or after learning was demon-strated experimentally (Zanone & Kelso, 1997). In particular, what we callhere tristable dynamics proved to be symmetric, as the intermediate at-tractor between inphase and antiphase was always accompanied by itssymmetry partner (e.g., �90° with �90°).


practiced limb pair. In particular, Figures 4C and 4D also suggestat least a transient destabilization of the antiphase pattern as aresult of learning the 90° phasing pattern.

Figure 5 shows the results of leg and arm scanning probes,carried out after practicing a 45° relative phase with the legs alone,for the same subject as in Figure 2. Figures 5A and 5B suggest thatthe practiced leg system is multistable after practice, exhibitingcoordination tendencies whose average values are about 4°, 55°,125°, and 180°. Again, practice created a stable state close to theto-be-learned phasing pattern, an unequivocal sign of learning.Second, the preexisting 90° pattern (cf. Figures 2A and 2B) van-ished completely, whereas the pattern at 180° remained quiteprominent, a finding already reported in previous work on biman-ual coordination (Zanone & Kelso, 1997). When the initial dy-namics is multistable, learning appears to involve a shift of analready-existing attractive state in the direction of the task require-ment. A novel finding shown in Figure 5 is that a pattern also

Figure 3. Initial scanning probes (Day 1) of the arm and leg coordination dynamics for a typical subject whopracticed a 75° relative (rel.) phase with the arms. A and B show probes of the arm system, whereas C and Dshow probes of the leg system. The left graphs display the performed (solid lines) and the required (dashed lines)relative phases. For ease of viewing, we joined together the 13 individual trials (labeled by plateau numbers) inwhich a single relative phase was required at random. The right graphs display the frequency distributions ofperformed relative phase across all phasing requirements. Both arm and leg probes revealed bistable dynamicsat about 0° and 180°. Panel A shows that a pattern around 125° was performed fairly stably, even if accidentally.Therefore, we set the learning task at 75°. deg � degrees.

Table 1Between-Trials Statistics (in Degrees) of Within-Trial MeanConstant Errors (CEs) and Standard Deviations for RelativePhase Performed in the First and Last Three Learning Trialsfor Three Typical Subjects

Subject Trials

CE SD

M SD M SD

1 First 3 49.10 10.66 13.61 8.44Last 3 4.85 5.53 4.05 0.29

2 First 3 103.933 9.92 15.76 8.71Last 3 22.71 0.68 8.29 1.32

3 First 3 52.34 4.07 16.78 2.60Last 3 �2.39 3.47 9.17 6.35


stabilized near 125°, although it had never been practiced at all.Thus, spontaneous transfer of learning seems to occur within thesame half of the phase diagram (i.e., between 0° and 180°, corre-sponding to right-lead phasing patterns), comparable to the transferdemonstrated across the two halves of the phase diagram (i.e.,from right-lead patterns to left-lead patterns and vice versa; seeZanone & Kelso, 1997). Again, symmetry arguments may beinvoked as a possible origin of this phenomenon, because 55° and125° are symmetrically distributed around 90°.

As for the nonpracticed arm system, Figures 5C and 5D displaya picture that is highly compatible with the one illustrated inFigures 5A and 5B for the leg system. All the indicators suggestthat a new attractive state appeared at about 45°, the to-be-learnedrelative phase, whereas the preexisting 90° attractive state essen-tially vanished (cf. Figures 2C and 2D). Good agreement betweenthe top and bottom rows of the figures suggests that transfer oflearning occurred spontaneously across initially multistable effec-

tor systems, given that the 45° pattern was practiced by the legsalone.

Figures 6A and 6B show the results of the postlearning probesfor the arm and leg systems for a subject who practiced a 75°relative phase with the arms. Both parts of the figure show com-parable results. After practice, stable states around 0° and 90° arenoticeable (close to the to-be-learned phasing) in the coordinationdynamics of both arm and leg systems, although practice was withthe arms alone. Comparison with the prelearning probes of thesame subject (cf. Figures 3A and 3B) suggests that learning andtransfer of learning occurred with practice.

Group Data

The individual data provide initial support for our hypothesisthat transfer of learning occurs spontaneously across comparable(i.e., symmetric) effector systems in both directions, from legs to

Figure 4. Final scanning probes (Day 2) of the leg and arm coordination dynamics for the same subject shownin Figure 1, who practiced 90° of relative (rel.) phase with the legs. A and B show probes of the leg system,whereas C and D show probes of the arm system. The left graphs display the performed (solid lines) and therequired (dashed lines) relative phases. For ease of viewing, we joined together the 13 individual trials (labeledby plateau numbers) in which a single relative phase was required at random. The right graphs display thefrequency distributions of performed relative phase across all phasing requirements. The leg and arm probesrevealed that the to-be-learned 90° pattern constitutes a novel attractive state of the coordination dynamics forboth the trained and untrained effector systems, attesting to learning and transfer of learning. deg � degrees.


arms and from arms to legs. In keeping with our previous work,learning and transfer of learning were assessed in terms of specificmodifications of the underlying coordination dynamics—evalu-ated by scanning probes of relative phase—in the direction of thetask requirement. Moreover, the form that such alterations takeappears to depend on the nature of the coordination dynamicsbefore any learning. We now consolidate these individual findingsby presenting the group results.

A general picture of the evolution of performance with practiceis provided in Figures 7A and 7B, for all subjects who practicedwith the arms or the legs, respectively. In both parts of the figure,the upper curve (solid line) represents the mean error in relativephase (i.e., the average difference between the produced and theto-be-learned relative phases), collapsed across learning tasks, as afunction of practice trials. The lower curve (dotted line) displaysthe corresponding mean within-trial standard deviation. For bothcurves, vertical bars indicate variability across subjects, encom-

passing �1 SD. The 40 scores per day are juxtaposed, so that thetrial numbering is continuous.

Figure 7A indicates that irrespective of actual phasing require-ment, mean error of arm performance (top solid curve) diminishesfivefold with practice to a value of about 7°. Variability (dashedcurve) decreases by one half, reaching a final standard deviationbelow 10°. For both scores, between-trials fluctuations andbetween-subjects variability (denoted by the vertical bars) alsodeclined. Figure 7B shows an even steeper improvement in botherror and variability scores for the legs, perhaps due to the largernumber of cycles per trial. These typical learning curves indicatea progressive stabilization of performance toward the criterionlevel. In particular, the functions presented are very similar tothose found in our earlier work on learning bimanual perceptuo-motor coordination (Zanone & Kelso, 1992, 1997). Figures 7A and7B indicate that regardless of which pattern is to be learned andwhich effector system is trained, subjects succeeded in learning the

Figure 5. Final scanning probes (Day 2) of the leg and arm coordination dynamics for the same subject shownin Figure 2, who practiced 45° of relative (rel.) phase with the legs. A and B show probes of the leg system,whereas C and D show probes of the arm system. The left graphs display the performed (solid lines) and therequired (dashed lines) relative phases. For ease of viewing, we joined together the 13 individual trials (labeledby plateau numbers) in which a single relative phase was required at random. The right graphs display thefrequency distributions of performed relative phase across all phasing requirements. The leg and arm probesrevealed that the to-be-learned 45° pattern constitutes a novel attractive state of the coordination dynamics forboth the trained and untrained effector systems, attesting to learning and transfer of learning. deg � degrees.


task within 80 trials of practice (1,760 individual cycles). Mostof the improvements in performance occurred in the first dailysession. Nevertheless, such change is relatively permanent, as seenin the stable performance on the second practice session, 1 daylater.4

How, then, do these changes in performance due to practicerelate to specific modifications of the underlying coordinationdynamics? First, consider the 4 subjects who practiced 75° or 90°with the arms. Figure 8A shows the relative frequency distribu-tions (in percentages) of all relative phases performed during thescanning probes before practice (dotted line) and after practice(solid line). Such histograms reflect the phasing patterns that areproduced most often, irrespective of the task requirement. Beforelearning, the arms performed relative phases near inphase andantiphase more frequently than other phasing patterns. After prac-tice, the main mode of the histogram is centered about the learningrequirement, whereas the antiphase pattern is almost never pro-

duced, even when it was required. This suggests that with practice,the to-be-learned pattern was performed not only when requested(in what actually amounts to only 7.6% of the overall cyclesperformed during all the scanning runs) but also for other taskrequirements. Such changes in the histograms are supported bystatistical analysis, �2(20, N � 4) � 70.20, p � .01.

Figure 8C shows the same data in another form, with specificreference to the task requirement. The mean error in relative phase(i.e., the difference between the produced and required relativephases) for the arm probes carried out before and after practice(dashed and solid lines, respectively) is plotted as a function of the

4 We demonstrated persistence of such improvements with practice(Zanone & Kelso, 1992) through a recall procedure carried out 1 week afterthe learning procedure. Comparable scores were obtained for all subjectsbetween the last practice trials and the recall trials.

Figure 6. Final scanning probes (Day 2) of the arm and leg coordination dynamics for the same subject shownin Figure 3, who practiced a 75° relative (rel.) phasing pattern with the arms. A and B show probes of the armsystem, whereas C and D show probes of the leg system. The left graphs display the performed (solid lines) andthe required (dashed lines) relative phases. For ease of viewing, we joined together the 13 individual trials(labeled by plateau numbers) in which a single relative phase was required at random. The right graphs displaythe frequency distributions of performed relative phase across all phasing requirements. The arm and leg probesrevealed that the coordination dynamics of both the trained and untrained effector systems were altered in thedirection of the to-be-learned pattern, attesting to learning and transfer of learning. deg � degrees.


required relative phase. A positive (negative) value means that therequired relative phase was overestimated (underestimated). Ver-tical bars encompass �1 between-subjects SD. In the prelearningprobe (dashed line), the mean error exhibits a humped shape as afunction of the required relative phase. Mismatch is lowest for the0° or 180° requirements, with a marked increase for intermediatevalues. The negative slope between 45° and 180° reflects a generalattraction to the antiphase pattern, because intermediate relativephases are overshot in that direction.5 Likewise, the negative slopebetween 0° and 15° suggests attraction to the inphase pattern. Suchattraction of nearby phasing requirements to 0° and 180° reflects

the stability of the inphase and antiphase patterns before learningand suggests that these patterns are attractive states of the under-lying coordination dynamics (Beek, Peper, & Stegeman, 1995;Carson et al., 1995; Fontaine et al., 1997; Kelso, 1984; Lee et al.,1995; Schoner et al., 1992; see Zanone & Kelso, 1992, for moredetails). After practice (solid line in Figure 8C), the mean error is

5 The negative slope in the error curve about a given value reflectsexactly the same phenomenon causing the plateaus in performance near aphasing value that can be seen in Figures 1–6, namely, attraction.

Figure 7. Performance improvements with practice. A: Practice with the arms. B: Practice with the legs. Thetop, solid curves represent the mean errors in relative phase (i.e., performed minus required), collapsed acrosssubjects, as a function of practice trials. The bottom, dashed curves represent the corresponding within-trialstandard deviations. Vertical bars denote between-subjects standard deviations. The general pattern of results forboth effector systems complies with typical learning curves, suggesting that the task was mastered by the endof the learning procedure. deg � degrees.


low not only around 0° but also around 90°. Moreover, a negativeslope spans all the way from 60° to 150°. Overestimation of therequired pattern below 90° and underestimation above it impliesthat the pattern actually performed is biased toward 90°, indicatingthat the learned state has become attractive to its neighbors. Inaccordance with the individual data, learning a new pattern ofcoordination involves stabilizing a value of the coordination dy-namics close to the task requirement.

Figures 8B (histogram) and 8D (error curve) show the results ofthe leg probes conducted before learning (dashed line) and afterlearning (solid line). Figure 8B shows that the initial frequency

distribution exhibits two dominant modes at 0° and 180°, whereasafter practice of the 75° or 90° pattern with the arm system, a newmode appears close to the to-be-learned value. Such a significantchange in the frequency distributions was confirmed statistically,�2(18, N � 4) � 34.78, p � .01. The negative slopes and zerocrossings seen in Figure 8D also suggest that 0° and 180° corre-spond to the initial attractive states of the leg coordination dynam-ics and that the pattern around 90° is stabilized with practice.Overall, these findings are quite comparable to those reported inFigures 8A and 8C regarding the arm coordination dynamics,although the leg system did not practice the task at all. The

Figure 8. Group changes with learning. Pre- and postlearning scanning probes of the arm and leg coordinationdynamics for subjects who practiced a 75° or 90° pattern with the arms. A and B show the frequency distributionsof the performed relative phases for all phasing requirements constituting probes of the arm and leg systems,respectively, before (dashed lines) and after (solid lines) practice of a 75° or 90° phasing with the arms. C andD show the average errors between the performed and required relative phases as a function of the phasingrequirement in the prelearning (dashed lines) and postlearning (solid lines) probes, collapsed across the samesubjects and effector systems. Vertical bars denote between-subjects standard deviations. Zero crossing of theerror curve with a negative slope is indicative of attractive states of the underlying coordination dynamics.Comparison of the results of pre- and postlearning probes in A and C suggests that learning involves stabilizingthe new pattern as an attractive state of the coordination dynamics of the practiced (arm) system. Comparisonof the results of pre- and postlearning scanning probes in B and D shows that learning also entails stabilizing thenew pattern as a stable state of the coordination dynamics of the unpracticed (leg) system. deg � degrees.


practiced pattern becomes a stable state of the dynamics of botheffector systems, a clear sign of transfer of learning.

Consider now the two subjects who practiced 75° or 90° withthe legs. Figures 9A and 9C show the frequency distributions andthe error curves for the relative phases performed by the legsduring the prelearning (dashed line) and postlearning (solid line)probes, respectively. The modes and zero crossing in each figuresuggest that prior to practice, the initial coordination dynamics forthe leg system was bistable at inphase and antiphase. After prac-tice, a new attractive state emerges close to the task requirement,whereas the antiphase pattern again appears to destabilize. Suchdifferences in the frequency histograms are confirmed statistically,

�2(17, N � 2) � 86.77, p � .01. These are the basic features oflearning a new coordination pattern that we have seen before.Figures 9B and 9D show the results of the probes for the armsystem conducted before learning (dashed line) and after learning(solid line). Although the pattern to be learned was not practicedby the arms, both parts of the figure show changes in the under-lying coordination dynamics analogous to those undergone by thelegs (cf. Figures 9A and 9C), again substantiated by statisticaltesting, �2(20, N � 2) � 71.30, p � .01. This result indicates thatspontaneous transfer occurred from the leg system to the armsystem, leading to similar modifications in their respective coor-dination dynamics.

Figure 9. Pre- and postlearning probes of the arm and leg coordination dynamics for subjects who practiceda 75° or 90° pattern with the legs. A and B show the frequency distributions of the performed relative phasesfor all phasing requirements constituting scanning probes of the leg and arm systems, respectively, before(dashed lines) and after (solid lines) practice of a 75° or 90° phasing with the arms. C and D show the averageerrors between the performed and required relative phases as a function of the phasing requirement in theprelearning (dashed lines) and postlearning (solid lines) probes, collapsed across the same subjects and effectorsystems. Vertical bars denote between-subjects standard deviations. Zero crossing of the error curve with anegative slope is indicative of attractive states of the underlying coordination dynamics. Comparison of theresults of pre- and postlearning probes in A and C shows that learning involves stabilizing the new pattern asa stable state of the coordination dynamics of the practiced (leg) system. Comparison of the results of pre- andpostlearning probes in B and D shows that learning also entails stabilizing the novel pattern as an attractive stateof the coordination dynamics of the unpracticed (arm) system. deg � degrees.


That learning and transfer involve similar changes in the attrac-tor layout was corroborated by a statistical analysis in which wecompared the mean error obtained with both limbs when therequired phasing pattern was set to 0°, 180°, and to the to-be-learned value (75° or 90°), across days of practice. A 2 � 2 � 3(Limb � Day � Pattern) analysis of variance with repeatedmeasures on day and pattern revealed that the effects of day andpattern were significant, F(1, 10) � 8.09, p � .02, and F(2, 20) �47.60, p � .01, respectively, as was their interaction, F(2, 20) �6.23, p � .01. Note that neither the effect of limb nor anyinteraction with limb was significant. Thus, differential effects dueto day and pattern were comparable across effector systems.

Taken together, Figures 8 and 9 and the related analyses confirmour main experimental hypotheses. First, irrespective of the systempracticing the task, learning involves alterations of the underlyingcoordination dynamics in the direction of the task requirement,such that the newly learned pattern becomes a stable state of thedynamics. Second, such modifications also occur spontaneously inthe dynamics of the effector system that did not practice thelearning task, suggesting automatic transfer of learning. One rea-son for transfer may be the similarity of both effector systems’dynamics before learning: Both were bistable at inphase andantiphase prior to practice. Moreover, these group data support ourprevious findings (Zanone & Kelso, 1992; see also Lee et al.,1995) that stabilizing a new attractive state may involve—at leasttemporarily—loss of stability of an initially stable state (i.e., 180°).

Figures 10A and 10B show the results of the probes obtained forthe 4 subjects who practiced 45°, regardless of which effectorsystem (arm vs. leg) actually practiced the task. Figure 10Adisplays the frequency histograms of the relative phase performedby the effector system that was actually exposed to training. Thedistribution suggests that before learning (dashed line), stablepatterns exist around 0°, 90°, and 180°. After practice (solid line),the most noticeable feature is the shift of the mode centered about90° toward 45°, the task requirement. Consonant with the individ-ual data shown in Figure 5A, learning led to the stabilization of anew attractive state at the required value of 45°, accompanied bythe virtual disappearance of the initially stable state at 90°. Thisfinding agrees with our previous results (Zanone & Kelso, 1997)showing that when the initial dynamics are multistable, learning anew pattern involves the shift of a preexisting nearby attractivestate toward the task requirement. The group data for the practicedeffector systems (see Figure 10A) also show a less prominentmode around 120°. As suggested in the individual data (Figure5A), it seems that learning also stabilizes one of the symmetrypartners of the learned 45° pattern, namely, 135°. This may be aphenomenon similar to the spontaneous transfer between symme-try partners with inverse sign (e.g., �135°) demonstrated in ourearlier study (Zanone & Kelso, 1997).

Figure 10B shows the frequency distributions of the performedrelative phase during scans of the effector system that was nottrained at 45°. The histogram for the prelearning probe (dottedline) exhibits two modes, at 0° and 180°, plus a less well-definedmode approximately centered around 110°. After learning 45° withthe other effector system, this intermediate mode shifts toward acentral value of 60°, close to the learning requirement. Thus, thefrequency distribution of the untrained effector systems matchesthat of the trained effector systems (cf. Figures 10A and 10B),suggesting spontaneous transfer of learning, regardless of whether

the arms or the legs actually practiced the to-be-learned relativephase. A test on the overall distribution data—that is, pooling allsubjects together—showed a significant effect of learning andtransfer, �2(18, N � 4) � 68.17, p � .01.

Figures 11A and 11B show the results of the scans obtained forthe 2 subjects who practiced the 135° phasing pattern, regardless ofwhich effector system (arm or leg) actually practiced the task. Forthe effector system that practiced the task (Figure 11A), the fre-quency histogram before practice (dashed line) indicates that thecoordination dynamics has a multistable character with attractivestates located about 0°, 90°, and 180°. After practice (solid line),the intermediate mode shifts to the value set as the learning task.Note that the initial 180° mode has apparently been incorporatedinto the new mode around 135°. Figure 11B shows a comparablefrequency distribution for the effector system that did not practicethe learning task. Once again, transfer of learning from the trainedto the untrained effector systems is evident, irrespective of whetherthe arms of the legs practiced the task. A test on the overall dataindicated a significant effect of learning and transfer, �2(18, N �2) � 48.12, p � .01.

In summary, the results for the subjects who learned 135° or 45°are quite consistent. Unlike the case of initially bistable dynamics(Figures 8 and 9), change consists of the shift of an already-existing attractive state (viz., 90°) toward the pattern to be learned.Such shifts have proven to be a typical route to learning associatedwith multistable coordination tendencies (Zanone & Kelso, 1997).It is interesting that the present results show that the intermediatestable pattern can be moved around in both directions (i.e., toward45° or 135°) in the space of the coordination variable, relativephase, to meet the learning task requirements.

Control Groups

The foregoing conclusions are valid insofar as the effects attrib-uted to learning and transfer of learning do not arise from the mereuse of the experimental equipment and/or from exposure to theseries of scanning runs used to probe the coordination dynamics ofthe two limb pairings.

Figures 12A and 12B show the frequency distributions of therelative phases performed by 6 control subjects during scanningprobes of the arm and leg systems, carried out on the first (dashedline) and second (solid line) day. Figure 12A shows that thehistograms are almost identical on both days. Figure 12B displaysthe same results regarding the leg system, indicating that theunderlying coordination dynamics remained virtually unchanged.A chi-square test (df � 20, N � 6) on the overall data for thecontrol groups yielded a nonsignificant value of 7.53 ( p � .05).The negligible differences exhibited across days for both effectorsystems in the control group further attest to the notion that theresults of the main experiment are a specific outcome of thelearning process.

Summary

The ensemble of results reported here provides new findings andcorroborates previous findings concerning the dynamics of learn-ing and transfer. On the one hand, we provide strong evidence thatlearning a new phase relationship with one effector system (thearms) automatically transfers to another effector system (the legs),


and vice versa. On the other hand, the basic mechanism throughwhich learning occurs is established further on two counts. First,we have shown that learning and transfer of learning involvesystematic modifications of the coordination dynamics of botheffector systems. Irrespective of differences in limb patterningbefore exposure to a novel learning task, the learned patternbecomes a novel attractive state of the underlying coordinationdynamics of both effector systems.6 Second, the coordinationdynamics prior to learning determines the form that the learningprocess may take. When coordination tendencies are initially bi-stable (i.e., the inphase and antiphase are attractive states), the

newly learned stable pattern is accompanied by the transient de-stabilization of a preexisting attractive state (i.e., 180°). Whencoordination tendencies are initially multistable (i.e., an attractivestate also exists about 90°), shifts (or drifts) toward the to-be-

6 Again, initial probes of the underlying coordination dynamics arecrucial to assert the novelty of a phasing pattern. The learned pattern wascertainly novel, because the task was set such that it did not correspond toany attractive states of the coordination dynamics that were present beforepractice.

Figure 10. Pre- and postlearning probes of the practiced and unpracticed effector systems for subjects whopracticed the 45° pattern. A and B show the frequency distributions of the performed relative phases for allphasing requirements used to probe the effector systems that did and did not practice the 45° phasing task,respectively. Comparison of the results of prelearning (dashed lines) and postlearning (solid lines) probesindicates that learning involves stabilizing the to-be-learned pattern as a stable state of the coordinationdynamics, irrespective of which effector system practiced the task. deg � degrees.


learned value occur, leaving preexisting coordination tendenciesmore or less unchanged.

General Discussion

An important issue in theories of skill acquisition and learningconcerns the nature of what is being learned. The present researchaddressed this issue from the perspective of coordination dynam-ics, a lawful representation that is hypothesized to govern how thecentral nervous system assembles coordinated patterns of activityon different levels of description. How abstract this representation

is may be ascertained by determining the effectiveness of transferor generalization from one (trained) effector system to another(untrained) effector system. Previous work on bimanual coordina-tion has established that learning involves modifications of thepreexisting coordination dynamics in the direction of the learningtask (Kelso, 1990; Schoner et al., 1992; Zanone & Kelso, 1992,1997) and that transfer may occur spontaneously between twocomponents within the same effector system (Zanone & Kelso,1994, 1997). Through the window of interlimb coordination, weconducted an experiment to test whether transfer of learning alsooccurs across different effector systems, causing similar alterations

Figure 11. Pre- and postlearning probes of the trained and untrained effector systems for subjects whopracticed the 135° pattern. A and B show the frequency distributions of the performed relative phases for allphasing requirements used to probe the effector systems that did and did not practice the 135° phasing task,respectively. Comparison of the results of prelearning (dashed lines) and postlearning (solid lines) probes showsthat learning involves stabilizing the to-be-learned pattern as a stable state of the coordination dynamics,irrespective of which effector system practiced the task. deg � degrees.


in their respective coordination dynamics. The task was to learn aspecific phase relationship through practice with the arms or thelegs. To assess modifications induced by learning and transfer, weevaluated the coordination dynamics of both effector systemsbefore and after practice through scanning probes aimed at reveal-ing underlying attractive or stable states of the coordination dy-namics (see also Tuller & Kelso, 1989; Yamanishi, Kawato, &Suzuki, 1980).

The results indicated that learning a novel relative phase withone effector system spontaneously transferred to the other, un-trained effector system. Not only was transfer seen as performanceimprovements in both systems when the to-be-learned phasing was

required but it was also revealed by qualitative modifications oftheir underlying coordination dynamics. That is, the dynamics ofboth the trained and untrained limb pairs exhibited either compa-rable phase transitions, themselves a signature of learning (Kelso,1990; Zanone & Kelso, 1992), or similar shifts in preexistingattractive states, a further, parametric sign of learning (Zanone &Kelso, 1997). Irrespective of the form taken by the learning pro-cess, the visually specified phasing pattern was learned and re-membered, creating a new attractive state in both the practiced andunpracticed coordination dynamics.

An important provision we took was that the pattern selected asa learning task did not coincide with already-existing attractive

Figure 12. Pre- and postlearning probes of both effector systems for control subjects who did not practice anyphasing pattern. A and B show the frequency distributions of the performed relative phases for all phasingrequirements used to probe the arm and leg systems, respectively, before (dashed lines) and after (solid lines)practice, for all the control subjects. Comparison of the results of pre- and postlearning probes for both effectorsystems shows negligible differences in the underlying coordination dynamics. deg � degrees.


states (or preferences) of the underlying coordination dynamics.Theoretically, before learning, any contribution to the coordinationdynamics due to the novel task requirement should compete withpreexisting, so-called intrinsic coordination tendencies. Such com-petitive interaction between behavioral task demands and individ-ual coordination tendencies is hypothesized to lead to the observedbias and increase in variability of the performed pattern. Thepresent results suggest that a common mechanism underlies learn-ing and transfer, namely, reduction of the competition that initiallyarises between task requirements and intrinsic coordination ten-dencies. How such competition is instantiated in the CNS is aninteresting question. It is now well established that different be-havioral phasing patterns have their expression in spatiotemporalpatterns of brain activity, quantified (using time-averaging tech-niques) in terms of spatial modes and their time-dependent ampli-tudes (e.g., Fuchs, Mayville, et al., 2000; Fuchs, Kelso, & Haken,1992; Jirsa et al., 1998; Kelso et al., 1992, 1998) or (in thefrequency domain) as patterns of power and coherence, particu-larly in the beta (15–30 Hz) range (Chen, Ding, & Kelso, 1999;Jantzen, Fuchs, Mayville, & Kelso, 2001; Mayville et al., 2001). Areasonable hypothesis is that competitive processes in learningmay be captured in terms of mode competition in the brain. Stillother evidence found using positron emission tomography indi-cates that activity in the parietal cortex remains high after transferhas occurred from fingers to arms in a sequencing task (Grafton,Hazeltine, & Ivry, 1998), suggesting that parietal areas are in-volved in generating the sequence at an abstract level independentof the effectors used. As expected, other neural areas, such as thesensorimotor cortex, are quite effector specific.

Scanning probes of subjects’ coordination abilities before andafter practice corroborate the idea that what is learned is not onlythe practiced coordination pattern but also an entire dynamics ofcoordination. The relevant coordination variable of these task-specific dynamics is the relative timing or phasing between thelimbs. We ruled out the alternate possibility that an absolute timeinterval between the limbs was actually learned and transferred,because the two effector systems performed the learning task andscanning probes at different movement frequencies. Were an ab-solute timing acquired, the learned and transferred relative phasesshould differ systematically, which was not the case here.

A closer look at the results indicates that although the effects oflearning and of transfer on the coordination dynamics are qualita-tively equivalent—namely, stabilization of an attractive state co-incident with the learning requirement—small but detectable quan-titative differences may be spotted in terms of strength andlocalization of attractive coordination patterns. First, the trans-ferred pattern (viz., pertaining to the untrained effector system)appears to be less stable than the learned attractor (viz., pertainingto the practiced system). This may be readily seen in terms ofvariability, with the learned pattern usually exhibiting a smallerstandard deviation than the transferred one. Moreover, the span ofthe negative slope effect, a sign of attraction to the learned patternin parameter space, is more limited for the transferred than for thelearned attractor. Second, whereas the learned pattern stabilizesvery close to the required phasing (generally within less than 10°),the transferred pattern is typically located a bit farther away. Notethat in the case of initially multistable dynamics, the shift of the90° pattern toward the required state is not always complete. Suchslight quantitative discrepancies between practiced and unprac-

ticed systems are to be expected given the limited amount ofpractice, the many superficial differences between arms and legs,and the different ways these anatomical structures could be con-trolled. The remarkable result, however, is the extent to which thetwo effector systems are similar in terms of changes in coordina-tion with learning.

The status of the antiphase pattern deserves closer scrutiny (seealso Fontaine et al., 1997; Lee, 1998). Except for the case oflearning a 45° phasing pattern, our findings indicate that the 180°pattern is performed less stably or accurately after learning, being(at least temporarily) drawn into the newly created basin of attrac-tion of the learned pattern. Why the temporary destabilization ofthe antiphase pattern appears more systematic here than in previ-ous studies is an open question. We have reported similar findingsin earlier work (Zanone & Kelso, 1992, 1997). In probes wheresubjects were asked to execute a large variety of relative phases,the antiphase pattern destabilized with the creation of a nearby(e.g., 90° or 135°) novel attractive state through learning. Incontrast, the 180° pattern appears to remain a stable state when the45° pattern is learned. This suggests a limit on the extent overwhich competitive processes may operate: When the newlylearned pattern is far enough from the intrinsic 180° phasingpattern, the latter does not diminish as an attractive state, eventhough it may become more variable. An important methodolog-ical point is that such a result cannot be interpreted as a historyeffect (Zanone & Kelso, 1997), meaning that when the targetrelative phase is incremented gradually, subjects tend to staylonger in the pattern currently performed regardless of the actualtask requirement. In the present study, we assigned the differentphasing requirements in a random and not in a stepwise fashion,thereby eliminating the possibility of hysteresis. Such methodolog-ical matters aside, there is absolutely no reason to expect thatsubjects, if asked to produce an antiphase pattern between the armsor between the legs spontaneously or from memory, could not doit. Generally speaking, it seems likely that the influence of thenewly learned pattern on one of the intrinsic coordination tenden-cies is transient and context dependent (see also Tsutsui, Lee, &Hodges, 1998, for another kind of evidence of context effects onlearning bimanual coordination).

At a conceptual level, the finding that similar alterations occurin the coordination dynamics of both the trained and untrainedeffector systems suggests that learning and transfer involve acommon mechanism—neurally instantiated, of course (cf. Graftonet al., 1998; Jantzen et al., 2001)—that exists at a rather abstractlevel of system functioning. In previous work (Zanone & Kelso,1997), we demonstrated that the realization of the learned phasingpattern was independent of any lead–lag relationship between thecomponents and independent of their kinematic implementation.Here, we found that the realization of such a pattern is also largelyindependent of the effector system used to perform the task (or,conversely, is shared by both effector systems). By definition, suchflexibility in the motor implementation of the same task is asignature of motor (or, as we prefer to call it, functional) equiva-lence (Kelso et al., 1984). Such equivalence may be possible onlybecause what is learned and remembered corresponds to task-levelattractive states of the coordination dynamics based on perceptionof the task. This statement is not intended to minimize specificneuromuscular–skeletal factors that have been shown to sculpt the


coordination dynamics (Carson & Riek, 1998; Jeka & Kelso, 1995;Kelso, Fink, DeLaplain, & Carson, 2001; Kelso & Jeka, 1992).

The idea that actions are specified in terms of attractive states ofan underlying coordination dynamics may shed light on how theCNS specifies a motor command. A command may have less to dowith a top-down prescription dictating the behavior of the individ-ual components than with the propensity of a complex system toexhibit but a limited set of attractive coordination states. Theparameters of the coordination dynamics are based on the ongoingintegration of information from a variety of sources that jointlyconstrain behavior and behavioral choice, including the perceptualrequirements of the task and the subject’s intentions, prior expe-riences, and movement history. In this picture, learning qua theemergence of novel collective states in response to new environ-mental constraints provides an essential means of behavioralflexibility.

In the framework of coordination dynamics, which factors in-fluence whether transfer occurs between different effector sys-tems? In our study, the practiced and unpracticed effector systemsinitially shared several characteristics. First, both the trained anduntrained systems are described by the dynamics of the sametask-specific coordination variable: relative phase. Thus, task andcoordination tendencies of both effector systems are captured inthe same space of variables. Second, although it varied on asubject-by-subject basis, each limb pair exhibited similar initialcoordination dynamics. Arm and leg systems were always bistable(i.e., attraction to inphase and antiphase only) or multistable (withanother attractive state). Thus, a second condition for extensivetransfer may be the similarity of the initial coordination dynamics.Although modified with learning, such similarity persisted evenwhen a novel coordination state was stabilized with learning andconstituted our main criterion for transfer. Third, the coordinationdynamics of both systems were symmetric; that is, the left andright components can be permuted without changing the underly-ing dynamics.7 Of course, to say that the arms or the legs form abilaterally symmetric system is trivial on the surface. In the presentcontext, however, symmetry requirements are more stringent, ontwo counts. On the one hand, the very coordination between thecomponents is symmetric; that is, the behavior of the right limbrelative to the left is perfectly equivalent to that of the left limbwith respect to the right. On the other hand, this remains so evenafter learning, because the spatiotemporal symmetry of the coor-dination dynamics is preserved. Further investigation awaits as towhich of the foregoing prerequisites is necessary for transfer oflearning to occur. One may wonder, for instance, whether there istransfer between a symmetric system—say, the arms—and anasymmetric system—say, the homolateral arm and leg.8

Finally, it may be useful to discuss briefly how the present workrelates to more classical views of skill acquisition and learning. Inmost, if not all, previous views the outcome of learning is ad-dressed in terms of abstract, task-specific entities such as schemas,images of achievement, and generalized motor programs (e.g.,Bartlett, 1932; Bernstein, 1967; R. A. Schmidt, 1975). For exam-ple, the aim of schema theory was to explain how variable expe-riences with a skill allow a learner to parameterize it in the form ofa generalized motor program (GMP). This generative, rulelikefeature of schema theory is intrinsic to even the most elementaryform of the coordination dynamics. Equation 1, for example,incorporates not only the so-called invariance properties of the

GMP but also the important dynamic features of multistability,metastability, state transitions, and hysteresis that are crucial forboth stability and flexibility (Kelso, 1997; Mitra et al., 1998). Forneurobehavioral dynamical systems (Kelso, 1991), these featurescorrespond to multifunctionality (different behavioral patterns forthe same parameter values), switching or decision making (onebehavioral pattern is selected over another at critical parametervalues), and a primitive kind of memory (the history of systembehavior affects the current state). Whereas data suggesting thatthe temporal structure of movement is preserved across variouskinds of parameterizations is used as prima facie evidence for aGMP (as it was for the earlier notion of coordinative structure; e.g.,Kelso et al., 1979; Turvey et al., 1978), coordination dynamicsrationalizes why this is so in terms of the fundamental concept ofstability. This issue is not merely semantic but has conceptual andmethodological consequences as well. For example, in coordina-tion dynamics loss of stability provides a selection mechanism inthe form of bifurcations or phase transitions for the emergence ofnovel behavioral patterns. Fluctuations or variability in a move-ment’s spatiotemporal structure are not errors or noise in theoutput of the motor program but rather a fundamental way for thesystem to test its own stability under the current circumstances.Thus, in coordination dynamics, fluctuations are an essential partof the decision-making mechanism that determines whether thesystem switches behavior (e.g., Kelso, Scholz, & Schoner, 1986;Schoner, Haken, & Kelso, 1986).

These theoretical differences notwithstanding, a persistent issuein cognitive science has been to define equivalence classes ofprocesses to understand how two different processes may beaccomplished by the same higher level mechanism or algorithm.Viewed in the context of perceptual–motor control and learning,this problem reduces to identifying the ensemble of coordinatedbehaviors that share the same task- or function-specific coordina-tion dynamics. By showing task level transfer, the present studyprovides an indication of just how abstract and generalizable thecoordination dynamics is. It may well be that coordination dynam-ics and its recent theoretical extensions—for example, those thatmodel observations of human brain and behavioral activity interms of dynamic neural fields (Fuchs, Jirsa, & Kelso, 2000; Jirsaet al., 1998; Jirsa & Haken, 1996; Jirsa & Kelso, 2000; Kelso,Fuchs, & Jirsa, 1999; Kelso, Jirsa, & Fuchs, 1999)—may mark thegenuine arrival of a new kinematics and dynamics for psycholog-ical states and cognitive processes (Churchland, 1988). We shallhave to wait and see.

7 See Footnote 3. Such symmetry intuitively reflects the commonsensi-cal notion that arms and legs are bilaterally symmetric.

8 In fact, there is evidence that learning overcomes initial asymmetries(in the form of a 25° phase lead at 1.0 Hz) between arms and legs (Brown,Carver, & Kelso, 1999).

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Received March 23, 2001Revision received September 11, 2001

Accepted November 2, 2001 �


Coordination dynamics of learning and transfer across different effector systems

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